Thus, the imaginary part accesses GPDs along the line \(x=\pm \xi \) ,
whereas the real part probes GPD integrals over \(x\) . The `diagonal' GPD, \(H(\xi ,\xi ,t=\Delta ^2)\)  is not a positive-definite probability
density, however it is a transition density with the momentum transfer \(\Delta _\perp \)  Fourier-conjugate to the transverse distance \(r\) 
between the active parton and the center-of-momentum of the spectator partons in the target [1]}.
Furthermore, the real part of
the Compton Form Factor is determined by a dispersion integral over the diagonal \(x=\pm \xi \)  plus the \(D\) -term [2]}, [3]}, [4]}, [5]}:
\(\Re \text{e}\left[\mathcal {H} (\xi ,t)\right] = \int _{-1}^1 dx \left\lbrace \left[H(x,x,t)+H(-x,x,t)\right]\left[\frac{1}{\xi -x} - \frac{1}{\xi +x}\right]+ 2 \frac{D(x,t)}{1-x} \right\rbrace \) 
